Charges are moving at the atomic level. In most materials the atomic currents (i.e. from spin & angular momentum) are randomly oriented so the net force is zero. However, in some materials, the atomic currents can become organized (correlated) on a macroscopic level and allow for a net magnetic force on the material.

Magnetism in permanent magnets results from the net magnetic field created by unpaired electron spins. These are not necessarily moving; some of the magnetism can come from orbital motion, but this is not the main effect. Electron spins are dipoles and there is a force law between these spins that is proportional to the magnetic moment of each and to the reciprocal of the cube of the separation. This force law is not F=qvxB.

Electron spins are dipoles and there is a force law between these spins that is proportional to the magnetic moment of each and to the reciprocal of the cube of the separation. This force law is not F=qvxB.

Actually, the strength of the magnetic field produced by the dipole varies inversely with the cube of distance and the potential energy of a dipole in a magnetic field is [itex]U = -\vec \mu \cdot \vec B[/itex] so the force exerted by one dipole on the other will vary as the gradient of U.

BTW - if we think about the magnetic moment of an electron classically then it amounts to a rotating charge, i.e. it constitutes an electrical current. Ultimately, these notions and forces between dipoles derive from the basic Lorentz force.